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arXiv · 2304.14899

On topological sigma-ideals

Sanjib Basu·Debasish Sen
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Abstract

The concept of $\mathcal S$-topological $\sigma$-ideal in measurable space $(X, \mathcal S)$ was introduced by Hejduk and using a theorem of Wagner on convergence of measurable functions characterized $\mathcal S$-topological $\sigma$-ideals. In this paper, we give a general construction of $\mathcal S$-topological $\sigma$-ideals from structures induced by $\sigma$-algebras and weakly upper semicontinuous $\omega$-small systems. We also show that instead of weak upper semicontinuity, if we use upper semicontinuity, we get $\mathcal S$-uniformizable $\sigma$-ideals. This generalizes the approach of Wagner and Wilczynski metrizing Boolean Lattice of measurable functions

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Sanjib Basu, Debasish Sen. 2023-04-28. On topological sigma-ideals. https://arxiv.org/abs/2304.14899

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